Isn't that what the USA basically does? That's why things are often banned in the EU before America, because the FDA (or whatever) normally has to prove it's bad before it gets pulled.
In the EU it's the other way around.
I could be wrong but I believe that's the general gist of it.
The FDA has tiers of regulation. Things like "supplements" are loosely regulated, while "pharmaceuticals" are much more highly regulated.
With supplements, the FDA pretty much lets things go until they start causing problems. DMAA was legal for a long time until people started having heart attacks. Melatonin, which is a straight-up hormone, is over-the-counter in the US, and it's by prescription only in Europe.
Now, if you're marketing something as a treatment for a disease, you have to have concrete data to back it up.
So it's very possible to have something that the FDA will let you sell as a supplement (i.e. there's no evidence that it's dangerous), but not make any claims about its efficacy (i.e. you can't say it will treat XYZ).
I experimented with nootropics at one point of my life (found them worthless, FYI), and it was funny how all of the labels just stated what it was, purity, and a blurb about the company selling it. There was no language whatsoever telling you what the supplement was for. Just a giant "PIRACETAM" label on the front.
That there are worse offenders of the principle that you have to show something to be harmful before you ban it doesn't make the behaviour of the FDA better.
It's hard to compare the EU to America just like that, especially since the EU is not a state, but you may be right. The EU makes incredibly arbitrary judgements and bans sometimes. Some European countries, however, fare much better when it comes to avoiding such blatant authoritarianism.
In the EU it's the other way around.
I could be wrong but I believe that's the general gist of it.